Enter the height and the angle of launch into the calculator to determine the minimum initial velocity to reach the height.

Minimum Initial Velocity Formula

The following equation is used to calculate the Minimum Initial Velocity.

Vmin = SQRT ( 2*G*H / Sin^2(a) )

  • Where Vmin is the minimum initial velocity to hit height H (m/s)
  • G is the acceleration due to gravity (9.81 m/s^2)
  • H is the height to be reached (m)
  • a is the angle of the launch (degrees)

What is a Minimum Initial Velocity?


A minimum initial velocity is the magnitude of a velocity needed in order for a projectile to reach a given height.

How to Calculate Minimum Initial Velocity?

Example Problem:

The following example outlines the steps and information needed to calculate Minimum Initial Velocity.

First, determine the height to be reached. In this example, the height to be reached is found to be 50m.

Next, determine the angle of the launch. For this problem, the angle of the launch is found to be 30 degrees.

Finally, calculate the Minimum Initial Velocity using the formula above:

Vmin = SQRT ( 2*G*H / Sin^2(a) )

Vmin = SQRT ( 2*9.81*50 / Sin^2(30deg) )

Vmin = 62.64 m/s